Machine learning-based method and system for predicting surface properties of solid substances

Abstract

The present invention provides a method and system for predicting the surface properties of solid substances based on machine learning, including: dividing all the termination structures of each crystal plane of the solid substance into a first structure and a second structure, calculating a first calculated surface energy function of the first structure as a training set to train a machine learning model; obtaining a second predicted stable structure in the second structure through the prediction model, calculating a second calculated surface energy function, and determining a first calculated stable structure according to all the calculated surface energy functions; moving the second predicted stable structure into the first structure, and then obtaining a second calculated stable structure through the above steps. If it is the same as the first calculated stable structure, it is the stable termination structure of the solid substance under the target chemical potential; using the stable termination structure and the corresponding calculated surface energy function to obtain the crystal morphology of the solid substance. A system for predicting the surface properties of solid substances and a data processing device for predicting the surface properties of solid substances are also provided.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning, and particularly relates to a method and a system for predicting the surface properties of solid substances. Background Art

[0002] Surface energy, as a fundamental surface property, determines the stability of the surface structure and is very important for the in-depth understanding of surface relaxation, reconstruction, and crystal growth. In addition, surface energy determines the equilibrium morphology of crystals. These surface characteristics are particularly important for the design and synthesis of new materials. Moreover, surface energy determines the stability and functionality of nanomaterials. Due to the unique properties brought by their high specific surface area, nanomaterials have been widely used in many application fields. For example, in heterogeneous catalysis, the morphology of nanocatalysts significantly affects the catalytic activity and selectivity of metal nanoparticles. Due to the limitations of experimental conditions and methods, it is very difficult to characterize surface energy and nanoparticle morphology at the atomic or molecular scale in experiments. Therefore, the research on these properties mainly relies on theoretical prediction. In particular, by combining density functional theory (DFT) calculations based on first principles with ab initio atom thermodynamics, surface energy associated with the chemical potential of elements under experimental conditions can be obtained. According to the Wulff theory, the crystal morphology can be further obtained.

[0003] In order to obtain systematic and accurate surface properties, it is necessary to examine as many Miller index crystal planes as possible. However, for multi-element systems, each Miller index crystal plane has multiple different surface terminations, and these surface termination structures need to be individually subjected to DFT calculations to determine their surface energy. However, according to the principle of thermodynamics, for each Miller index crystal plane examined, usually only the most stable (lowest surface energy) surface termination will appear on the Wulff morphology, and only the surface structures that appear on the Wulff morphology are more worthy of further attention. For multi-element systems with complex structures, different surface terminations generate a huge unknown exploration space. Enumerative DFT calculations for the huge exploration space waste expensive computing resources, and the time cost and labor cost are extremely high, which limits the systematic research on the basic surface properties of a large number of solid materials with complex structures. Therefore, although automated calculation tools have been developed, high-throughput surface energy calculations still only stay in single-element crystals. For multi-element crystals, existing work replaces surface energy with cleavage energy calculations and greatly simplifies from a model perspective to reduce the calculation cost. Rapid prediction through model establishment is a solution, but existing technologies are only applicable to single-element crystals. In addition, the energy obtained by existing prediction technologies is only under ideal conditions and cannot be correlated with experimental conditions. Therefore, more efficient theoretical prediction and theoretical calculation of solid surface energy and crystal morphology are urgent problems to be solved. Summary of the Invention

[0004] In view of the above problems, the present invention uses a machine learning model to predict the surface energy associated with the chemical potential of elements, and proposes a method for predicting the surface properties of solid substances, which specifically includes: an initialization step, dividing the surfaces of each unit cell of the solid substance into a first surface or a second surface, marking all possible surface termination structures of the first surface as first structures, and marking all possible surface termination structures of the second surface as second structures; a model training step, performing density functional theory calculations on the first structures to obtain a first calculated surface energy function, constructing a training data set with the first calculated surface energy function and the structural features of the first structures, and training a machine learning model to obtain a surface structure prediction model; a stable structure acquisition step, predicting the predicted surface energy function of the second structures with the surface structure prediction model, marking the second structures as second predicted stable structures and second predicted unstable structures according to the first calculated surface energy function and the predicted surface energy function, performing density functional theory calculations on the second predicted stable structures to obtain a second calculated surface energy function, determining a stable surface structure according to the first calculated surface energy function and the second calculated surface energy function, and taking it as the calculated stable structure of the solid substance; an iteration step, marking the second predicted stable structures as first structures, and sequentially calling the model training step and the stable structure acquisition step for iterative operations until the calculated stable structure obtained in the current round of operations is exactly the same as the calculated stable structure obtained in the previous round, and taking the calculated stable structure obtained in the current round as the stable surface termination structure of the solid substance; a morphology prediction step, obtaining the crystal morphology of the solid substance with the stable surface termination structure and the calculated surface energy function of the stable surface termination structure.

[0005] In the method for predicting the surface properties of a solid substance according to the present invention, in the initialization step, the symmetry of the bulk unit cell of the solid substance is obtained, and according to the symmetry, the cell surface with a Miller index less than or equal to a specified index threshold is used as the first surface.

[0006] In the method for predicting the surface properties of a solid substance according to the present invention, according to the symmetry, the cell surface with a Miller index greater than the index threshold and less than a specified maximum Miller index is used as the second surface.

[0007] In the method for predicting the surface properties of a solid substance according to the present invention, a simulated X-ray diffraction spectrum of the bulk unit cell of the solid substance is obtained, and the cell surface that belongs to the characteristic diffraction peak in the simulated X-ray diffraction spectrum and has a Miller index greater than the index threshold is used as the second surface.

[0008] In the method for predicting the surface properties of a solid substance according to the present invention, a periodic slab model with central symmetry of the upper and lower surfaces is used as the surface model to obtain the possible surface termination structures of the first surface and the possible surface termination structures of the second surface.

[0009] The method for predicting the surface properties of a solid substance according to the present invention, wherein the machine learning model is a Gaussian process regression model, and the kernel function of the Gaussian process regression model is a Gaussian kernel function.

[0010] The method for predicting the surface properties of a solid substance according to the present invention, wherein the projector augmented wave (PAW) method is used to describe the electron-ion interaction of the solid substance, and all the calculated surface energy functions are obtained by using the generalized gradient approximation (GGA) and the PBE exchange-correlation functional.

[0011] The present invention also provides a system for predicting the surface properties of a solid substance, including: an initialization module for dividing the surfaces of each unit cell of the solid substance into a first surface or a second surface, marking all possible surface termination structures of the first surface as first structures, and marking all possible surface termination structures of the second surface as second structures; wherein the Miller index of the first surface is less than or equal to an index threshold, the Miller index of the second surface is greater than the index threshold and less than a specified maximum Miller index, or the Miller index of the second surface is greater than the index threshold and the second surface belongs to a characteristic diffraction peak in the simulated X-ray diffraction pattern; a termination structure acquisition module for obtaining the stable surface termination structure of the solid substance under the chemical potential of the target element, including: a model training module, a stable structure acquisition module, and an iteration module; the model training module is used to train a surface structure prediction model, obtain a first calculated surface energy function by performing density functional theory calculations on the first structures, construct a training data set with the first calculated surface energy function and the structural characteristics of the first structures, and train a machine learning model to obtain the surface structure prediction model; the stable structure acquisition module is used to obtain the calculated stable structure of the solid substance; predict the predicted surface energy function of the second structures through the surface structure prediction model, mark the second structures as second predicted stable structures and second predicted unstable structures according to the first calculated surface energy function and the predicted surface energy function, perform density functional theory calculations on the second predicted stable structures to obtain second calculated surface energy functions, determine the stable surface structure according to the first calculated surface energy function and the second calculated surface energy functions, and use it as the calculated stable structure of the solid substance; the iteration module is used to obtain the stable surface termination structure of the solid substance, by marking the second predicted stable structures as first structures, and sequentially calling the model training module and the stable structure acquisition module for iterative operations until the calculated stable structure obtained in the current round of operations is exactly the same as the calculated stable structure obtained in the previous round, and using the calculated stable structure obtained in the current round as the stable surface termination structure; a morphology prediction module for obtaining the crystal morphology of the solid substance with the stable surface termination structure and the calculated surface energy function corresponding to the stable surface termination structure.

[0012] The present invention also provides a computer-readable storage medium storing computer-executable instructions, characterized in that when the computer-executable instructions are executed, the method for predicting the surface properties of solid substances based on machine learning as described above is implemented.

[0013] The present invention also provides a data processing device, including the computer-readable storage medium as described above. When the processor of the data processing device retrieves and executes the computer-executable instructions in the computer-readable storage medium, the prediction of the surface properties of solid substances based on machine learning is performed. Description of the Drawings

[0014] Figure 1 is a flowchart of the method for predicting the surface properties of solid substances based on machine learning according to the present invention.

[0015] Figure 2 is a result graph of the calculation cost percentage and the success rate of an embodiment of the present invention.

[0016] Figure 3 is a result graph of the surface energy function of an embodiment of the present invention.

[0017] Figure 4 is a result graph of the Wulff morphology of an embodiment of the present invention.

[0018] Figure 5 is a schematic diagram of the data processing device according to the present invention. Detailed Embodiments

[0019] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific implementation methods described herein are only used to explain the present invention and are not used to limit the present invention.

[0020] Currently, the theoretical prediction of the surface energy and crystal morphology of a solid at a specified chemical potential mainly relies on the enumeration method. The complexity of this method lies in that all surface termination structures in the exploration space need to be calculated one by one to determine the surface termination structure with an advantage in energy competition and its surface energy, and further obtain the Wulff morphology. Therefore, the disadvantage of this method is that it will waste a large amount of computing resources and human resources when applied to complex structures.

[0021] The present invention provides a more efficient high-throughput calculation method for surface properties to overcome the above problems. The main object of the present invention is to provide an automated high-throughput calculation method by combining high-throughput DFT calculations, ab initio atom thermodynamics, and machine learning techniques, using significantly reduced computational costs while maintaining DFT accuracy to obtain the surface energy and crystal morphology of a solid under specified element chemical potentials; the secondary object is to use a machine learning model based on structural descriptors and optimized online to quickly predict the surface energy related to element chemical potentials and determine the potentially stable surface termination structures to assist in achieving the main object. The core technologies of the present invention include: low-index surface termination structures as the initial training set; structural features based on the chemical coordination environment of surface atoms as the feature vectors for establishing the machine learning model; using an iterative process to establish and optimize the machine learning model; during the iterative process, using the machine learning model to predict, determining the potentially stable surface termination structures, and using DFT calculations for accurate sampling to obtain high-precision results.

[0022] The machine learning-based solid surface property prediction method of the present invention includes:

[0023] Step 1: Perform DFT calculations on the bulk unit cell to be studied, thereby relaxing both the atomic positions and the lattice.

[0024] Step 2: Find the symmetry of the bulk unit cell and determine the initial cell surfaces required for model training according to the symmetry and the specified index threshold. In the present invention, data for training the model is obtained from low-index surfaces with Miller indices less than or equal to the index threshold, and the target cell surfaces for surface energy prediction using the trained prediction model are high-index surfaces with Miller indices greater than the index threshold. In an embodiment of the present invention, high-index surfaces with all Miller indices greater than the index threshold and less than the specified maximum Miller index are used as the target cell surfaces. In another embodiment of the present invention, calculate the X-ray diffraction (XRD) spectrum of the bulk unit cell, and based on the characteristic diffraction peaks in the simulated XRD spectrum, use the cell surface with characteristic diffraction peaks and Miller indices greater than the specified index threshold as the target cell surface.

[0025] Step 3: Generate all possible surface termination structures for each of the initial cell surfaces and target cell surfaces according to the Miller indices determined in Step 2.

[0026] Step 4: Calculate the chemical coordination environment of the surface atoms of all the generated possible surface termination structures to obtain a dataset of surface structure features.

[0027] Step 5: Perform DFT calculations on each surface termination structure of the simple low-index surfaces one by one to obtain the surface energy function, and use these surface termination structures as the initial training set for machine learning, and the remaining surface termination structures as the test set.

[0028] Step 6: Based on the surface structure features in the training set and the surface energy function calculated by DFT, train a machine learning model to obtain a model of the relationship between the surface structure descriptor and the surface energy function;

[0029] Specifically, construct a data set for machine learning using the surface structure features in the training set and the surface energy function calculated by DFT. Among them, the surface structure feature descriptors constitute the feature vector, and the surface energy function is expressed as:

[0030]

[0031] where G slab represents the Gibbs free energy of the surface model, N i represents the number of species i in the model, μ i represents the value of the chemical potential of species i at temperature T and pressure p, and A represents the surface area of the slab model; taking the binary system A x B v as an example, the above formula can be written as:

[0032]

[0033] where the relationship between μ A and μ B can be expressed by the following formula:

[0034]

[0035] where represents the Gibbs free energy of the bulk phase model; considering that the contributions of configurational entropy, vibrational energy, and pV term to the surface energy are very small and can be ignored, therefore, the Gibbs free energy G can be approximated as the total energy E obtained by DFT calculation. At this time, the surface energy function of A x B y can be expressed by the following formula:

[0036]

[0037] where and are known terms, while is an unknown term. Obtaining the value of this part can obtain the surface energy function. Therefore, in the embodiments of the present invention, the calculated by DFT is used as the target value for model training; the machine learning regression model used is Gaussian process regression (GPR), and the kernel function is the Gaussian kernel function.

[0038] Step 7: Apply the trained model to the test set, i.e., the remaining unsampled surface termination structures, predict their surface energy functions, and determine the surface termination structures that may be stable at the target elemental chemical potential based on the surface energy functions calculated by DFT for the sampled structures and the surface energy functions predicted by the model for the unsampled structures;

[0039] Step 8: Perform DFT calculations on the surface termination structures that have not been sampled among the potentially stable surface termination structures, and determine the stable surface termination structures at the target elemental chemical potential based on all the surface energy functions calculated by DFT;

[0040] Step 9: When all the stable surface termination structures determined by the surface energy functions calculated by DFT in two consecutive rounds are exactly the same, proceed to the next step; otherwise, move the newly sampled surface termination structures and their surface energy functions from the test set to the training set, and return to Step 6 to start the next round of iteration;

[0041] Step 10: Based on the stable surface termination structures and their surface energies at the specified chemical potential obtained from the above iterative process, substitute them into the Wulff construction theory to obtain the Wulff morphology.

[0042] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0043] Figure 1 is a flowchart of the method for predicting the surface properties of solid substances based on machine learning according to the present invention. As Figure 1 shown, a method for predicting the surface properties of a solid based on machine learning provided by the present invention includes the following steps:

[0044] Step S1: Use the VASP software to perform DFT calculations on the bulk unit cell to be studied, relax the atomic positions and the lattice, and obtain the total energy of the bulk unit cell;

[0045] Step S2: Automatically find the symmetry of the bulk unit cell using the pymatgen program and calculate its XRD spectrum; determine the low-index surfaces to be investigated according to the Miller indices less than or equal to the specified index threshold (such as 1), and determine the high-index surfaces to be investigated according to the characteristic diffraction peaks in the XRD spectrum and the Miller indices greater than the specified threshold; in other embodiments of the present invention, the high-index surfaces to be investigated can also be determined according to the specified index threshold (such as 1) and the specified maximum Miller index (such as 3);

[0046] Step S3: Automatically generate all possible surface termination structures for each crystal plane according to the determined Miller index crystal planes, and the surface model used is a periodic slab model with central symmetry on the upper and lower surfaces;

[0047] Step S4: Calculate the surface atomic chemical coordination environment of all generated surface termination structures to obtain a dataset of surface structure features;

[0048] Step S5: The periodic slab model of low-index surfaces usually has higher symmetry and fewer atoms, and requires lower computational costs. At the same time, the surface structure features of low-index surfaces can uniformly cover the feature space. Therefore, use the VASP software to perform DFT calculations on each surface termination structure of simple low-index surfaces one by one to obtain the surface energy function, and use these surface termination structures as the initial training set for machine learning to improve the efficiency of this technical solution. The remaining surface termination structures are used as the test set;

[0049] Step S6: Construct a dataset for machine learning using the surface structure features in the training set and the surface energy function calculated by DFT; specifically, the surface structure feature descriptors form a feature vector. In this embodiment, the surface structure feature descriptors used are ΔN 0 and the surface coordination unsaturation d suc ; Taking the binary system A x B v as an example, ΔN 0 can be expressed as:

[0050]

[0051] where N A and N B represent the numbers of species A and B in the surface model respectively, A represents the surface area of the surface model, and ΔN 0 represents the degree of A-rich and B-rich in the surface model per unit area; the surface coordination unsaturation d suc can be expressed as:

[0052]

[0053] where is the generalized atomic valence of atom i in the surface model, is the generalized atomic valence that atom i should have in the bulk phase, A represents the surface area of the surface model, and d suc represents the degree of surface atomic coordination unsaturation per unit area; the surface energy function is expressed as:

[0054]

[0055] where G slab represents the Gibbs free energy of the surface model, N A and N B represent the numbers of species A and B in the model respectively, μ A and μ Brespectively represent the values of the chemical potentials of species A and B at temperature T and pressure p, and A represents the surface area of the slab model, where μ A and μ B are related as follows:

[0056]

[0057] where, represents the Gibbs free energy of the bulk model; considering that the contributions of configurational entropy, vibrational energy, and the pV term to the surface energy are very small and can be ignored, thus, the Gibbs free energy G can be approximated as the total energy E obtained from DFT calculations. At this time, the surface energy function of A x B y can be expressed as follows:

[0058]

[0059] where, and are known terms, while is an unknown term. Obtaining the value of this part can yield the surface energy function. Therefore, in this embodiment, the calculated by DFT is used as the target value for model training; training a machine learning model, the machine learning regression model used is Gaussian Process Regression (GPR), and the kernel function is the Gaussian kernel function; training the Gaussian Process Regression model to obtain a model of the relationship between surface structure descriptors and surface energy functions;

[0060] Step S7: Apply the trained model to the test set, that is, the remaining unsampled surface termination structures, predict their surface energy functions, and determine the possibly stable surface termination structures at the target element chemical potential based on the surface energy functions calculated by DFT of the sampled structures and the surface energy functions predicted by the model of the unsampled structures; Gaussian Process Regression has excellent performance in evaluating uncertainty. Therefore, when searching for possibly stable surface termination structures, the uncertainty predicted by the model will be considered, thereby increasing the energy search space and avoiding premature convergence of the iterative process;

[0061] Step S8: Identify unsampled surface termination structures among the potentially stable surface termination structures, perform DFT calculations using the VASP software, and determine the stable surface termination structures at the chemical potential of the target element based on the surface energy functions of all DFT calculations; in this embodiment, all DFT calculations use the generalized gradient approximation (GGA) and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional, and the electron-ion interaction is described using the projector augmented wave (PAW) method; it should be noted that the feasibility of this technical route is not limited by the setting of calculation parameters;

[0062] Step S9: When all the stable surface termination structures determined by the surface energy functions calculated by DFT in two consecutive rounds are exactly the same, proceed to Step S10; otherwise, move the newly sampled surface termination structures and their surface energy functions from the test set to the training set, and return to Step S6 to start the next round of iteration;

[0063] Step S10: Based on the stable surface termination structures and their surface energies obtained from the above iterative process, substitute them into the Wulff construction theory to obtain the Wulff morphology.

[0064] Specifically, taking four iron-based binary systems as examples, for χ-Fe5C2, the initial training set includes the (001), (010), (100), (011), (10-1), (101), and (110) surfaces; for θ-Fe3C and o-Fe3B, the initial training set includes the (001), (010), (011), (100), (101), and (110) surfaces; for β-FeSi2, the initial training set includes the (001), (011), (100), and (101) surfaces. Figure 2 The performance of this technical solution was evaluated. The horizontal axis is the percentage of the calculation cost, with 100% corresponding to the calculation cost of calculating one by one using the enumeration method. The vertical dashed line corresponds to the optimal value of the calculation cost reduction, which is an ideal situation that cannot be achieved. The vertical axis is the success rate based on the surface termination with an exposed area greater than 1% on the Wulff morphology, and 100% corresponds to the Wulff morphology obtained by calculating one by one using the enumeration method. As Figure 2As shown in the figure, taking the number of DFT calculations as the standard, after one iteration, the calculation costs of each system are between 25% and 40%, and the success rate has reached over 60%. Among them, for χ-Fe5C2 and o-Fe3B, the success rates reach 88.5% and 72.7% respectively. When the iteration process converges, the calculation costs of each system are between 40% and 55%, and the success rate has reached over 85%. Among them, for χ-Fe5C2, θ-Fe3C and o-Fe3B, the success rates reach 100%, 100% and 94% respectively. Because the calculation costs of the low-index surfaces that make up the initial training set are relatively low, the calculation costs will be even lower when taking the DFT computer time as the standard. For example, for χ-Fe5C2, the calculation cost of the first iteration is only 33%, and the calculation cost is approximately 44% when the iteration process converges. Figure 3 The surface energy functions obtained for χ-Fe5C2 at the first iteration and when the iteration converges are given. Among them, the differences from the surface energy functions obtained by the prior art are specifically marked. Due to the high sampling success rate and the fact that the final energy comes from DFT calculations, the lowest surface energy of each crystal plane obtained is basically the same as the result of the enumeration method. After only one iteration, the obtained surface energy function is already very close to the result obtained by the prior art. When the iteration converges, there is only a slight error of less than 0.02 J / m 2 for the (221) surface, which can be ignored. Figure 4 The Wulff morphologies obtained for χ-Fe5C2 at the first iteration, when the iteration converges, and those obtained by the prior art are given. Due to obtaining accurate surface energy, after only one iteration (33% calculation cost), the obtained Wulff morphology is already basically the same as the result obtained by the prior art. The above results show that the present invention can achieve high-throughput prediction and calculation of the solid surface properties with the accuracy of DFT calculations, as well as significantly reduced calculation resources and human resources.

[0065] Figure 5 is a schematic diagram of the data processing device of the present invention. As Figure 5As shown in the figure, the embodiments of the present invention further provide a computer-readable storage medium and a data processing device. The computer-readable storage medium of the present invention stores computer-executable instructions. When the computer-executable instructions are executed by the processor of the data processing device, the above-mentioned method for predicting the surface properties of solid substances based on machine learning is implemented. Those of ordinary skill in the art can understand that all or part of the steps in the above method can be completed by a program instructing relevant hardware (such as a processor, FPGA, ASIC, etc.). The program can be stored in a readable storage medium, such as a read-only memory, a magnetic disk, or an optical disc. All or part of the steps of the above embodiments can also be implemented using one or more integrated circuits. Correspondingly, each module in the above embodiments can be implemented in the form of hardware, for example, by an integrated circuit to implement its corresponding function, or in the form of a software functional module, for example, by a processor executing a program / instruction stored in a memory to implement its corresponding function. The embodiments of the present invention are not limited to any specific form of the combination of hardware and software.

[0066] The present invention has the following obvious substantial features and remarkable advantages:

[0067] 1. The present invention theoretically predicts and performs high-throughput calculations on the solid surface energy and crystal morphology, which helps to overcome the dilemma of accurately characterizing these solid surface properties experimentally.

[0068] 2. The present invention uses a Gaussian process regression model to predict the surface energy associated with the elemental chemical potential, thereby extending the rapid prediction of surface energy from single-element crystals to multi-element systems and from ideal conditions to experimental conditions.

[0069] 3. The present invention uses low-index surfaces as the initial training set and uses an iterative method to optimize the Gaussian process regression model online, and performs accurate sampling with DFT calculations, avoiding blind enumeration and trial and error. Moreover, the whole process can be implemented in the form of pure computer-readable program code. Therefore, the present invention can significantly reduce the required computing resources and human resources, obtain calculation results with DFT accuracy, truly improve the R & D efficiency, and extend the theoretical calculation research of surface properties to complex structures.

[0070] 4. The present invention selects structural features based on the chemical coordination environment of surface atoms, which well conforms to the chemical origin of surface energy and makes the established machine learning model have a certain interpretability.

[0071] The above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Those of ordinary skill in the relevant technical field can make various changes and deformations without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention shall be defined by the claims.

Claims

1. A method for predicting the surface properties of solid substances based on machine learning, characterized in that, Including: Initialization step: Divide the surfaces of each unit cell of the solid substance into a first surface or a second surface, mark all possible surface termination structures of the first surface as first structures, and mark all possible surface termination structures of the second surface as second structures; Model training step: Perform density functional theory calculations on the first structures to obtain a first calculated surface energy function, construct a training data set with the first calculated surface energy function and the structural characteristics of the first structures, and train a machine learning model to obtain a surface structure prediction model; Stable structure acquisition step: Use the surface structure prediction model to predict the predicted surface energy function of the second structures, mark the second structures as second predicted stable structures and second predicted unstable structures according to the first calculated surface energy function and the predicted surface energy function, perform density functional theory calculations on the second predicted stable structures to obtain a second calculated surface energy function, determine the stable surface structures according to the first calculated surface energy function and the second calculated surface energy function, and use them as the calculated stable structures of the solid substance; Iteration step: Mark the second predicted stable structures as first structures, and sequentially call the model training step and the stable structure acquisition step for iterative operations until the calculated stable structures obtained in the current round of operations are exactly the same as those obtained in the previous round, and use the calculated stable structures obtained in the current round as the stable surface termination structures of the solid substance; Morphology prediction step: Obtain the crystal morphology of the solid substance with the stable surface termination structures and the calculated surface energy functions of the stable surface termination structures.

2. The method for predicting the surface properties of a solid substance according to claim 1, characterized in that, In the initialization step, obtain the symmetry of the bulk unit cell of the solid substance, and according to the symmetry, use the cell surfaces with Miller indices less than or equal to the specified index threshold as the first surface.

3. The method for predicting the surface properties of a solid substance according to claim 2, characterized in that, According to the symmetry, use the cell surfaces with Miller indices greater than the index threshold and less than the specified maximum Miller index as the second surface.

4. The method for predicting the surface properties of a solid substance according to claim 2, wherein Obtain the simulated X-ray diffraction spectrum of the bulk unit cell of the solid substance, and use the cell surfaces that belong to the characteristic diffraction peaks in the simulated X-ray diffraction spectrum and have Miller indices greater than the index threshold as the second surface.

5. The method for predicting the surface properties of a solid substance according to claim 1, characterized in that, Use a periodic slab model with centrosymmetry of the upper and lower surfaces as the surface model to obtain the possible surface termination structures of the first surface and the possible surface termination structures of the second surface.

6. The method for predicting the surface properties of a solid substance according to claim 1, wherein The machine learning model is a Gaussian process regression model, and the kernel function of the Gaussian process regression model is a Gaussian kernel function.

7. The method for predicting the surface properties of a solid substance according to claim 1, characterized in that, Adopt the projector augmented wave method to describe the electron-ion interaction of the solid substance, and use the generalized gradient approximation and the PBE exchange-correlation functional to obtain the first calculated surface energy function and the second calculated surface energy function.

8. A solid substance surface property prediction system based on machine learning, characterized in that, Including: An initialization module for dividing the surfaces of each unit cell of a solid substance into a first surface or a second surface, marking all possible surface termination structures of the first surface as a first structure, and marking all possible surface termination structures of the second surface as a second structure; wherein, the Miller index of the first surface is less than or equal to an index threshold, the Miller index of the second surface is greater than the index threshold and less than a specified maximum Miller index, or the Miller index of the second surface is greater than the index threshold and the second surface belongs to a characteristic diffraction peak in the simulated X-ray diffraction pattern; A termination structure acquisition module for acquiring the stable surface termination structure of the solid substance at the chemical potential of a target element; including: a model training module, a stable structure acquisition module, and an iteration module; The model training module is used to train a surface structure prediction model. By performing density functional theory calculations on the first structure to obtain a first calculated surface energy function, constructing a training data set with the first calculated surface energy function and the structural characteristics of the first structure, and training a machine learning model to obtain the surface structure prediction model; The stable structure acquisition module is used to acquire the calculated stable structure of the solid substance; predicting the predicted surface energy function of the second structure through the surface structure prediction model, marking the second structure as a second predicted stable structure and a second predicted unstable structure respectively according to the first calculated surface energy function and the predicted surface energy function, performing density functional theory calculations on the second predicted stable structure to obtain a second calculated surface energy function, determining the stable surface structure according to the first calculated surface energy function and the second calculated surface energy function, and taking it as the calculated stable structure of the solid substance; The iteration module is used to acquire the stable surface termination structure of the solid substance. By marking the second predicted stable structure as the first structure, sequentially calling the model training module and the stable structure acquisition module for iterative operations until the calculated stable structure obtained in the current round of operations is exactly the same as the calculated stable structure obtained in the previous round, and taking the calculated stable structure obtained in the current round as the stable surface termination structure; A morphology prediction module for obtaining the crystal morphology of the solid substance with the stable surface termination structure and the calculated surface energy function corresponding to the stable surface termination structure.

9. A computer-readable storage medium storing computer-executable instructions, characterized in that, When the computer-executable instructions are executed, the method for predicting the surface properties of a solid substance based on machine learning as described in any one of claims 1 to 7 is implemented.

10. A data processing device, including the computer-readable storage medium as described in claim 9. When the processor of the data processing device retrieves and executes the computer-executable instructions in the computer-readable storage medium, it performs the prediction of the surface properties of a solid substance based on machine learning.

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